Answer: Range: y = {-7.5, -5, 10, 15}
Step-by-step explanation:
Domain is "x" and range is "y" f(x)
Replace the x's in the equation with each given value:
[tex]f(x)=3x-\dfrac{x}{2}\qquad \qquad \text{when}\ x={-3, -2, 4, 6}\\\\\\\\f(-3)=3(-3)-\bigg(\dfrac{-3}{2}\bigg)\\\\\\.\qquad =-9+\dfrac{3}{2}\\\\\\.\quad =\dfrac{-18}{2}+\dfrac{3}{2}\\\\\\.\quad =\large\boxed{-\dfrac{15}{2}}[/tex]
[tex]f(-2)=3(-2)-\bigg(\dfrac{-2}{2}\bigg)\\\\\\.\qquad =-6+1\\\\\\.\qquad =\large\boxed{-5}[/tex]
[tex]f(4)=3(4)-\bigg(\dfrac{4}{2}\bigg)\\\\\\.\qquad =12-2\\\\\\.\qquad =\large\boxed{10}[/tex]
[tex]f(6)=3(6)-\bigg(\dfrac{6}{2}\bigg)\\\\\\.\qquad =18-3\\\\\\.\qquad =\large\boxed{15}[/tex]
The range of the function with the specified domain of {-3, -2, 4, 6} is {-15/2, -5, 10, 15}.
The student asks: if fx=3x-x/2 find the range if the domain is {-3,-2,4,6}. To find the range of the function f(x) = 3x - x/2, we will evaluate the function for each value in the given domain and record the corresponding outputs. This function simplifies to f(x) = (5/2)x when you combine like terms.
For x = -3, f(-3) = (5/2)(-3) = -15/2.
For x = -2, f(-2) = (5/2)(-2) = -10/2 = -5.
For x = 4, f(4) = (5/2)(4) = 20/2 = 10.
For x = 6, f(6) = (5/2)(6) = 30/2 = 15.
7-10 =
How do I write it as an expression using a positive exponent
Answer:
-3
Step-by-step explanation:
7-10=-3
What is the lcm of 24,36,and, 60?
Answer: 360
Step-by-step explanation:
LCM is least common multiple. In other words, what number is divisible by 24, 36, and 60?
Factor each term. See what they have in common and then multiply the common term by all of the leftovers.
24 36 60
∧ ∧ ∧
12 2 12 3 12 5
They all have a 12 in common. The leftovers are 2, 3, & 5.
So, the LCM is 12 × 2 × 3 × 5 = 360
A gas engine is 6% efficient. What portion of a 12 gallon tank of gas is wasted?
Answer:
282/25
Step-by-step explanation:
[tex]efficient \: = 12 \times \frac{6}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{72}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{18}{25 } \\ so \: \\ west \: = 12- \frac{18}{25} \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{282}{25} \: \: gallon[/tex]
plzzzz...
mark it as a brilliant answer
The wasted portion of gallon tank will be "[tex]\frac{282}{25}[/tex]". A further solution is provided below.
Given:
Efficient percent = 6%Number of gallon = 12Now,
The efficient portion will be:
= [tex]12\times \frac{6}{100}[/tex]
= [tex]\frac{72}{100}[/tex]
= [tex]\frac{18}{25}[/tex]
hence,
The wasted portion of gallon tank will be:
= [tex]12-\frac{18}{25}[/tex]
= [tex]\frac{282}{25} \ gallon[/tex]
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How do you solve this?
Sergei estimated 149% of 67 by performing the following steps. Which statement is true?
(70)(150%)
- (70)(100% + 50%)
- (70)(100%) + (70)(50%)
- (70)(1)+ (70) )
- 70+35
- 105
The estimate is less than the actual answer because the percent and the number were both rounded down.
The estimate is less than the actual answer because the percent and the number were both rounded up.
The estimate is greater than the actual answer because the percent and the number were both rounded down.
The estimate is greater than the actual answer because the percent and the number were both rounded up.
Answer: Last option.
Step-by-step explanation:
In order to estimate the percent "n" of a number"x", you need easy numbers to work with, therefore you can round "n" and "x" up or down; but it is important to remember that this estimation does not give you an exact value.
You can observe that Sergei's first step was to round 149% and 67 up, getting this result:
[tex]=105[/tex]
To verify if this estimate is less or greater than the actual answer, we can find the actual answer. This is:
[tex]\frac{67*149}{100}=99.83[/tex]
Therefore, we can conclude that the estimate is greater than the actual answer because the percent and the number were both rounded up.
Answer:
D
Step-by-step explanation:
I did it on Edgen 2020
A regular prism has two congruent rectangles as its bases. How can one base be transformed to carry onto the other?
One base must be translated to carry onto the other base
One base must be rotated to carry onto the other base
It is impossible to carry one base onto the other base
One base must be reflected to carry onto the other base
Answer:
One base must be translated to carry onto the other base
Step-by-step explanation:
A regular prism has two congruent rectangles as its bases. Since the bases of the prism are congruent and oriented the same way, neither reflection nor rotation will work to carry one base onto the other. It doesn't matter how many sides a geometric shape has.
Therefore the correct option is:
One base must be translated to carry onto the other base.
Solve a = 2x + 6xz for x
To solve the equation a = 2x + 6xz for x, isolate x on one side of the equation by following the steps: subtract 6xz from both sides, factor out x, and divide both sides by (2 + 6z).
To solve the equation a = 2x + 6xz for x, we need to isolate x on one side of the equation. Here are the steps:
Start with the equation: a = 2x + 6xz
Subtract 6xz from both sides: a - 6xz = 2x
Factor out x on the right side: a - 6xz = x(2 + 6z)
Divide both sides by (2 + 6z): (a - 6xz) / (2 + 6z) = x
Therefore, the solution for x is x = (a - 6xz) / (2 + 6z).
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Kyle gave 2/7 of his money to his wife and spent 3/5 of the remainder. If he had $300 left, how much money did he have at first?
Answer:
Kyle gave 2/7th of his money to his wife and spent 3/5 of the remainder. If he had $300 left, the money had by Kyle at first is $1050
Solution:
Step 1:
Consider “x” as the money which Kyle had initially.
From question, Kyle gave 2/7th of his money to his wife. So the remaining money left with Kyle is given as,
[tex]= 1 - \frac{2}{7}[/tex]
[tex]= \frac{7 - 2}{7} = \frac{5}{7}[/tex] ----- eqn 1
Now the remaining money left with Kyle is 5/7th.Given that Kyle spent 3/5 of the remaining money.
Now the remaining money left with Kyle is given as
[tex] = 1 - \frac{3}{5} = \frac{5 - 3}{5} = \frac{2}{5}[/tex]
Now kyle is left with $300, which is 2/5th of the initial money x .
We get equation as
[tex]\frac{2}{5} x=300[/tex]
2x = 1500
x = 750
Now Kyle is left with 750$ which is 5/7th of the initial amount x.( by using eqn 1)
We get equation as
[tex]\frac{5}{7} x = 750[/tex]
5x = 5250
x = 1050
So the amount had by Kyle at first is $1050
Final answer:
Working backward from the $300 Kyle had after spending and giving some away, we find that the original amount of money was $1050, which is determined by reversing the operations he performed on his money.
Explanation:
To solve how much money Kyle had at first, we need to work backwards from the amount he had left ($300) after he spent some and gave some to his wife. First, we determine how much was left before he spent the 3/5 of the remainder.
Let's denote Kyle's initial amount of money as x. The equation representing what Kyle did with his money is
x - (2/7)x = Remaining Amount After Giving to Wife
Kyle then spends 3/5 of this remaining amount, and is left with $300, so we can represent this as:
(1 - 3/5)(Remaining Amount After Giving to Wife) = $300
Substituting the first equation into the second we get:
(1 - 3/5)(x - (2/7)x) = $300
Simplifying, we find that (2/5)(5/7)x = $300.
This simplifies down to:
(2/5)(5/7)x = (10/35)x = $300
Finally, solving for x, we multiply both sides by the reciprocal of (10/35),
x = $300 × (35/10)
x = $300 × 3.5
x = $1050
So, Kyle originally had $1050.
For which equation would x = 12 be a solution?
12 ÷ x > 12
12 - x ≥ 4
12x < 200
Answer:
12x < 200
Step-by-step explanation:
Substitute x = 12 into the left side of the inequality and compare with right side, that is
12 ÷ 12 = 1 < 12 ← not a solution
12 - 12 = 0 < 4 ← not a solution
12 × 12 = 144 < 200 ← this is a solution
12 less than m is no less than 132
The number will be "m = -120".
Let,
The number be "m".According to the question,
The expression will be:
→ [tex]m-12=-132[/tex]
By adding "12" both sides of the expression, we get
→ [tex]m-12+12=-132+12[/tex]
→ [tex]m = -120[/tex]
Thus the response above is right.
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To solve the given statement '12 less than m is no less than 132', we set up the inequality m - 12 ≥ 132. Adding 12 to both sides, we find that m ≥ 144.
Explanation:Given the statement '12 less than m is no less than 132', we can set up an inequality to represent this relationship: m - 12 ≥ 132. To solve for m, we can add 12 to both sides of the inequality: m ≥ 132 + 12. Simplifying, we find that m ≥ 144. So, any value of m that is greater than or equal to 144 will satisfy the given statement.
2(4+2x) > 5x+5
Solve the inequality
Answer:
x < 3
Step-by-step explanation:
Apply distributive property on the left of the inequality to get rid of the parenthesis:
8+4x > 5x+5
subtract 4x from both sides to group all terms with x on the right:
8 > 5x-4x+5
8 > x +5
Now subtract 5 from both sides to collect all numerical terms on the left:
8 - 5 > x
3 > x
Therefore the solution to the inequality are of those real numbers strictly smaller than 3.
The inequality can be written as x < 3 or also as we had it initially: 3 > x
Notice that the opening of the angle symbol is always facing the number 3 , meaning that 3 is the larger of the two numerical objects that are compared.
a cheetah can run 27 m per second that means that a travels 27 m in 1 second at this rate how far can it travel in 8 Seconds
Answer:
5.4 m/s2
Step-by-step explanation:
Answer: 216 meters per 8th second
Step-by-step explanation:
do 27 times 8 it will give you 216
how many halves are in 5 and 1/2
Answer:
There are 11 halves in 5 1/2
Step-by-step explanation:
The simplest way to solve this is by drawing 5 squares and a half a square.
Next would to count all the halves and there would be 11.
This is the super simple and easiest way to solve this.
If you have any questions feel free to ask in the comments.
There are 11 halves in 5 and 1/2.
What is a fraction?A fraction is a number that is represented as a quotient where the numerator is divided by the denominator.
What is half in mathematics?
Two equal parts of one whole thing. In fraction form, half can be written as 1/2.
How to solve this problem?We have to find the number of halves in 5 and 1/2. We know that there are 2 halves of one whole thing. For 5 as a whole number, the number of halves would be,
5 × 2 = 10. Then, there are 10 halves in 5. Notice that there is one more 1/2 in 5 and 1/2. We can conclude that there are 10 + 1 = 11 halves in 5 and 1/2.
Therefore, there are 11 halves in 5 and 1/2.
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when the outliers are removed how does the mean change?
1 dot on 50
2 dots on 72
1 dot on 74
1 dot on 76
1 dot on 78
3 dots in between 78 and 80
1 dot on 80
1 dot between 80 and 82
3 dots on 82
the mean decreases by 1.9
the mean decreases by 2.4
the mean decreases by 1.9
there are no outliers
Answer: The mean increases by 2.1
Step-by-step explanation:
According to the given description (dots are denoting the frequency for each value), the given data is :-
50 , 72, 72 , 74, 76 , 78 , 79 , 79 , 79 80, 81, 82, 82, 82
[Note - We take 79 as the value between 78 and 80, 81 as between 80 and 82 ]
Mean = [tex]\overline{x}_1=\dfrac{\text{Sum of observations}}{\text{No. of observations}}[/tex] (1)
[tex]=\dfrac{1066}{14}=76.1428571429\approx76.1[/tex]
First Quartile: [tex]Q_1=[/tex] Median of the lower half ( 50 , 72, 72 , 74, 76 , 78 , 79 )
= 74
Third Quartile: [tex]Q_3=[/tex] Median of the upper half ( 79 , 79 80, 81, 82, 82, 82 )
= 81
Interquartile range (IQR)=[tex]Q_3-Q_1=81-74=7[/tex]
According to the IQR rule,
Upper limit = [tex]1.5\times IQR+Q_3=1.5\times7+81=91.5[/tex]
Lower limit = [tex]Q_1-1.5\times IQR=74-1.5\times7=63.5[/tex]
Since 50 < 63.2 , so 50 is outlier .
When 50 is removed from the data , the new data will be 72, 72 , 74, 76 , 78 , 79 , 79 , 79 80, 81, 82, 82, 82
Mean = [tex]\overline{x}_2=\dfrac{\text{Sum of observations}}{\text{No. of observations}}[/tex]
[tex]=\dfrac{1016}{13}=78.1538461538\approx78.2[/tex] (2)
Change in mean from (1) and (2)
[tex]\overline{x}_2-\overline{x}_1\\\\=78.2-76.1=2.1[/tex]
Hence, the mean increases by 2.1.
Answer:
2.4
Step-by-step
A number q plus 8 is less than or equal to 15
Answer:
q≤7
Step-by-step explanation:
q+8≤15
1) Subtract 8 from both sides:
q≤7
Answer:
[tex]\displaystyle 7 ≥ q; q + 8 ≤ 15[/tex]
Step-by-step explanation:
q + 8 ≤ 15
- 8 - 8
_______
[tex]\displaystyle q ≤ 7[/tex]
** The above answer is written in reverse, which is the exact same result.
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Guys need help ASAP With these two problems
Answer:
Question1: 58660
Question 3: 7244
Step-by-step explanation:
Question 1: My 5 is worth 50,000 means the number will start with 5 and will be between 50,000 and 60,000, thus will have 5 digits in total
My 8 is worth 8,000 means the next number is 8
One of my 6s is worth 60 means there is more than one 6. One 6 is worth 60 and the other is 10times as much so 600. The other digit is a 0. So those 3 together are 660.
The entire number is 58660
Question 3: The number has 4 digits:
My 7 is worth 7000 so the number will be between 7,000 and 8,000.
My 2 is worth 200 so.
One of my 4s is worth 40. So this means there is another 4.
The other number is 1/10 of 40, which is 4.
The total is 7244
the lines below are parallel if the slope of the green line is -2 what is the slope of the red line
Answer:
-2
Step-by-step explanation:
Since they are parallel, they have the same slope. This will be true for any set of lines.
Is 16:14 in 64:60 eqivulant
Answer:
No they are not.
Step-by-step explanation:
16 and 64 [Scale factors of ¼ and 4]
14 and 60 [Scale factors of 7⁄30 and 4 2⁄7]
When we are talking about ratios, quantities must go into each other EVENLY.
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stadium costs 1.6 billion dollars to build. It is 2 million square feet. What is the unit rate of cost/sq. Ft?
Answer:
$1.25 per sq ft
Step-by-step explanation:
2,000,000,000 ÷ 1,600,000,000 = 1.25
write an expression for the amount of money (in dollars) in n nickels
Answer:
m1.00 +n0.20
Step-by-step explanation:
20 times 5 equal one dollar
The amount of money in n nickels can be expressed as 5n.
Explanation:The expression for the amount of money in n nickels can be written as 5n. Since each nickel is worth 5 cents, multiplying the number of nickels by 5 will give the amount in dollars. For example, if you have 3 nickels, the expression would be 5 x 3 = 15 dollars.
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If K={(x, y) I x-y=5), is Set K a function?
Yes
No
Answer:
NO!
NO NUMBER VARIABLES CAN BE CALLED A FUNCTION
20/30 as a decimal rounded to the nearest tenth
Answer:
1.5
Step-by-step explanation:
Answer:
0.7
Step-by-step explanation:
30 cannot be multiplied to give a power of 10, so to find the decimal you have to divide: 2/3 = 2/3 + 2 ÷ 3
2 divided by 3 is 0.6666666... It is a recurring decimal.
However it is not practical to use recurring decimals in calculations, so the decimal is usually rounded off to 2 or 3 decimal places depending on the accuracy required for the answer.
How many user must mike recruit in order for him to steam movies for free? The service costs $43.75 a month, but mikes rate is reduced by $1.25 for each new subscriber that he gets to sign up.
Answer:
35 subscribers
Step-by-step explanation:
Divide $43.75 by $1.25.
$43.75/$1.25 = 35
For each subscriber he gets, his service goes down by $1.25.
Since 35 * $1.25 = $43.75, for 35 new subscribers, his service will go down by $43.75.
He pays $43.75, so if the service goes down by $43.75, he will pay nothing since $43.75 - $43.75 = 0.
Answer: 35 subscribers
Follow below steps:
To determine how many users Mike must recruit for him to stream movies for free, we need to set up a simple algebraic equation. Mike's service costs $43.75 per month, and for each new subscriber he recruits, his rate is reduced by $1.25. Let's say the number of users Mike needs to recruit is represented by x.
The cost reduction for recruiting x users would be $1.25x. To get a free service, the total cost reduction must equal the monthly service cost of $43.75. Thus, the equation is $1.25x = $43.75.
To solve for x, we divide both sides by $1.25:
x = $43.75 / $1.25
x = 35
Therefore, Mike must recruit 35 new subscribers to stream movies for free.
64.8 divided by 7 showing using long division
Answer:
9.257
Step-by-step explanation:
7 goes into 64 nine times with the remainder of 1. Bring the decimal point up and the 8 down. 7 goes into 18 two times with the remainder of 4. 7 goes into 40 5 times with the remainder of 5. 7 goes into 50 7 times. That equals 9.257.
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KA
To divide 64.8 by 7 using long division, calculate how many times 7 can be subtracted from each part of the number 64.8 in sequence. This results in the final answer of 9.25.
Explanation:To find 64.8 divided by 7 using long division, first write down 64.8 with a division bar over it and 7 on the left side of the bar. You would write:
7 | 64.8
Next, ask: How many times does 7 go into 64? This is 9 times since 7 times 9 is 63. Record the 9 above the line and record the product (63) below 64. Subtract 63 from 64 to get 1.
Bring down the 8 (from 64.8) to the right of the 1. Now you have 18. Ask how many times does 7 go into 18? This is 2 times. So you add the digit 2 next to 9 on top of the bar. 7 times 2 is 14.
Subtract 14 from 18 to get 4. As the decimal point should be straight up from where it is in the 64.8, record a decimal point.
Now, since there's no more numbers to bring down, you can add a 0 to 40. 7 goes into 40, 5 times. Therefore, we add 5 next to the 2 after the decimal point. So, 64.8 divided by 7 is 9.25.
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How many times dose 24 go into 1,392
Answer:
58
Step-by-step explanation:
1392/24=58
Answer: 24 goes into the number 1,392, 58 times
Verbal expression for r+4
Answer:
a number increased by 4
Step-by-step explanation:
r = a number
increased by four = +4
four more than the number R
Step-by-step explanation: with the word than you would flip it to r+4
-6(1 - 5m) = 114
what is the answer?
Answer:
m=4
Step-by-step explanation:
A city has a rectangular park that is 143 feet by 32 feet. There is a grassy field with a width of 30 feet. Next to the field there's a flower bed with the width of 2 feet. What is the area of the park in square feet?
Answer: 4,576 ft
Step-by-step explanation: multiply 143 and 32 together.
The size of the field and the flower bed is just extra information they are using to trick you.
Answer:
[tex]4576 feet^2[/tex]
Step-by-step explanation:
Length of the park = 143 feet
Width of park = 32 feet
Area of rectangular park = [tex]Length \times Breadth[/tex]
= [tex]143 \times 32[/tex]
= [tex]4576 feet^2[/tex]
Hence the area of the park in square feet is [tex]4576 feet^2[/tex]
22. Write the equation in Slope-Intercept form of the line with an x-intercept of 2
and a y-intercept of -1.
Answer:
y = [tex]\frac{1}{2}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, 0) and (x₂, y₂ ) = (0, - 1) ← coordinates of intercepts
m = [tex]\frac{-1-0}{0=2}[/tex] = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
The y- intercept is - 1 ⇒ c = - 1
y = [tex]\frac{1}{2}[/tex] x - 1
PLLZZZZ SOLVE!!!!
A toy company is redesigning its packaging for model cars. Resize it so that 1/2 inch on the old packaging represents 1/3 inch on the new package. Find the length of the new package. The old package measures 2 inches
Answer:
The length of the new package is 4/3 in
Step-by-step explanation:
we know that
1/2 inch on the old packaging represents 1/3 inch on the new package
so
using proportion
Find out the length of the new package if the old package measures 2 inches
Let
x ----> the length of the new package
[tex]\frac{(1/3)}{(1/2)}\frac{new}{old}=\frac{x}{2}\frac{new}{old} \\\\x=(2/3)/(1/2)\\\\x=\frac{4}{3}\ in[/tex]
therefore
The length of the new package is 4/3 in